Problem: Simplify the following expression: $ a = \dfrac{-7t + 4}{t - 2} + \dfrac{-5}{6} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{-7t + 4}{t - 2} \times \dfrac{6}{6} = \dfrac{-42t + 24}{6t - 12} $ Multiply the second expression by $\dfrac{t - 2}{t - 2}$ $ \dfrac{-5}{6} \times \dfrac{t - 2}{t - 2} = \dfrac{-5t + 10}{6t - 12} $ Therefore $ a = \dfrac{-42t + 24}{6t - 12} + \dfrac{-5t + 10}{6t - 12} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-42t + 24 - 5t + 10}{6t - 12} $ $a = \dfrac{-47t + 34}{6t - 12}$